Recent advancements in single-cell technologies allow characterization of experimental perturbations at single-cell resolution. While methods have been developed to analyze such experiments, the application of a strict causal framework has not yet been explored for the inference of treatment effects at the single-cell level. Here we present a causal-inference-based approach to single-cell perturbation analysis, termed CINEMA-OT (causal independent effect module attribution + optimal transport). CINEMA-OT separates confounding sources of variation from perturbation effects to obtain an optimal transport matching that reflects counterfactual cell pairs. These cell pairs represent causal perturbation responses permitting a number of novel analyses, such as individual treatment-effect analysis, response clustering, attribution analysis, and synergy analysis. We benchmark CINEMA-OT on an array of treatment-effect estimation tasks for several simulated and real datasets and show that it outperforms other single-cell perturbation analysis methods. Finally, we perform CINEMA-OT analysis of two newly generated datasets: (1) rhinovirus and cigarette-smoke-exposed airway organoids, and (2) combinatorial cytokine stimulation of immune cells. In these experiments, CINEMA-OT reveals potential mechanisms by which cigarette-smoke exposure dulls the airway antiviral response, as well as the logic that governs chemokine secretion and peripheral immune cell recruitment.